相对运动变质量力学系统Appell方程的广义Lie对称性导致的广义Hojman守恒量

贾利群; 孙现亭; 张美玲; 张耀宇; 韩月林

doi:10.7498/aps.63.010201

摘要

研究相对运动变质量完整系统Appell方程的广义Lie对称性及其直接导致的广义Hojman守恒量. 在群的无限小变换下，给出相对运动变质量完整系统Appell方程广义Lie对称性的确定方程；得到相对运动变质量完整系统Appell方程广义Lie对称性直接导致的广义Hojman守恒量的表达式. 最后，利用本文结果研究相对运动变质量完整约束的三自由度力学系统问题.

关键词:

Generalized Lie symmetry and generalized Hojman conserved quantity of Appell equations for a variable mass holonomic system in relative motion are studied. The determining equation of generalized Lie symmetry of Appell equations for a variable mass holonomic system in relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from generalized Lie symmetry for a variable mass holonomic system in relative motion is gained. Finally, the problem of dynamical system with three degree of freedom is studied by using the results of this paper.

Keywords:

作者及机构信息

1.
平顶山学院电气信息工程学院, 平顶山 467000;

2.
常州市第一中学数学教研组, 常州 213003;

3.
江南大学理学院, 无锡 214122

基金项目: 国家自然科学基金（批准号：11142014）和江苏省普通高校研究生科研创新计划项目（批准号：CXLX12_0720）资助的课题.

Authors and contacts

1.
School of Electric and Information Engineering, Pingdingshan University, Pingdingshan 467000, China;

2.
Mathematics Teaching and Research Group, Changzhou No.1 High School, Changzhou 213003, China;

3.
School of Science, Jiangnan University, Wuxi 214122, China

Funds: Project supported by the National Natural Science Foundation of China(Grant No. 11142014), and the Scientific Research and Innovation Plan for College Graduates of Jiangsu province, China (Grant No. CXLX12_0720).

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施引文献

[1]	Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica 47 63
[2]	Huang W L, Cai J L 2012 Acta Mech. 223 433
[3]	Luo S K, Li Z J, Li L 2012 Acta Mechanica 223 2621
[4]	Cai J L 2012 Nonlinear Dyn. 69 487
[5]	Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[6]	Li Z J, Luo S K 2012 Nonlinear Dyn. 70 1117
[7]	Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[8]	Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[9]	Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 73 357
[10]	Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[11]	Luo S K, Li Z J, Peng W, Li L 2013 Acta Mechanica. 224 71
[12]	Li L, Luo S kai 2013 Acta Mechanica 224 1757
[13]	Lou Z M, Mei F X, Chen Z D 2012 Acta Phys. Sin. 61 110204 (in Chinese) [楼智美, 梅凤翔, 陈子栋 2012 61 110204]
[14]	Chen X W, Liu C M, Li Y M 2006 Chin. Phys. 15 470
[15]	Xie Y L, Jia L Q, Luo Shao-Kai 2011 Chin. Phys. B 20 010203
[16]	Jia L Q, Han Y L, Zhang M L, Wang X X 2013 Journal of Pingdingshan University 28(2) 27 (in Chinese) [贾利群, 韩月林, 张美玲, 王肖肖 2013 平顶山学院学报 28(2) 27]
[17]	Mei F, X 2000 Beijing Inst.Technol. 9 120
[18]	Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[19]	Li Y C, Xia L L, Wang X M, Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese) [李元成, 夏莉丽, 王小明, 刘晓巍 2010 59 3639]
[20]	Zheng S W, Jia L Q, Yu H S 2006 Chin. Phys. 15 1399
[21]	Jia L Q, Xie Y L, Zhang Y Y, Yang X F 2010 Chin. Phys. B 19 110306
[22]	Wang X X, Zhang M L, Han Y L, Jia L Q 2012 Acta Phys. Sin. 61 200203 (in Chinese) [王肖肖, 张美玲, 韩月林, 贾利群 2012 61 200203]
[23]	Sun X T, Han Y L, Wang X X, Zhang M L, Jia L Q 2012 Acta Phys. Sin. 61 200204 (in Chinese) [孙现亭, 韩月林, 王肖肖, 张美玲, 贾利群 2012 61 200204]
[24]	Hojman S A 1992 J. Phys. A: Math. Gen. 25 291
[25]	Xu X J, Mei F X, Zhang Y F 2006 Chin. Phys. 15 19
[26]	Ge W K, Zhang Y 2005 Acta Phys. Sin. 54 4985 (in Chinese) [葛伟宽, 张毅 2005 54 4985]
[27]	Wang X X, Sun X T, Zhang M L, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 124501
[28]	Lin P, Fang J H, Pang T 2008 Chin. Phys. B 17 4361
[29]	Ding N, Fang J H, Chen X X 2008 Chin. Phys. B 17 1967
[30]	Fang J H 2010 Chin. Phys. B 19 040301
[31]	Zhang N X, Fang J H, Lin P, Pang T 2008 Commun. Theor. Phys. 49 1145
[32]	Zhang M J, Fang J H, Lin P, Lu K, Pang T 2009 Commun. Theor. Phys. 52 561
[33]	Xia L L, Li Y C, Wang X J 2009 Commun. Theor. Phys. 51 1073
[34]	Zhang M L, Sun X T, Wang X X, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 110202
[35]	Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[36]	Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Journal of Yunnan University 34 664 (in Chinese) [张美玲, 王肖肖, 韩月林, 贾利群 2013 云南大学学报 34 664]
[37]	Wang X X, Sun X T, Zhang M L, Han Y L, Jia L Q 2012 Chin. Phys. B 21 050201
[38]	Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[39]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量(北京: 北京理工大学出版社)]

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